1. INTRODUCTION

The last decade has seen an explosive increase in both the volume and
the accuracy of data obtained from cosmological observations. The
number of techniques available to probe and cross-check these data has
similarly proliferated in recent years.

Theoretical cosmologists have not been slouches during this time,
either. However, it is fair to say that we have not made comparable
progress in connecting the wonderful ideas we have to explain the
early universe to concrete fundamental physics models. One of our
hopes in these lectures is to encourage the dialogue between
cosmology, particle physics, and string theory that will be needed to
develop such a connection.

In this paper, we have combined material from two sets of TASI
lectures (given by SMC in 2002 and MT in 2003). We have taken the
opportunity to add more detail than was originally presented, as well
as to include some topics that were originally excluded for reasons of
time. Our intent is to provide a concise introduction to the basics
of modern cosmology as given by the standard
"CDM" Big-Bang
model, as well as an overview of topics of current research interest.

In Lecture 1 we present the fundamentals of
the standard cosmology,
introducing evidence for homogeneity and isotropy and the
Friedmann-Robertson-Walker models that these make possible. In
Lecture 2 we consider the actual state of
our current universe, which
leads naturally to a discussion of its most surprising and problematic
feature: the existence of dark energy. In
Lecture 3 we consider the
implications of the cosmological solutions obtained in Lecture 1 for
early times in the universe. In particular, we discuss thermodynamics
in the expanding universe, finite-temperature phase transitions, and
baryogenesis. Finally, Lecture 4 contains a
discussion of the problems
of the standard cosmology and an introduction to our best-formulated
approach to solving them - the inflationary universe.

Our review is necessarily superficial, given the large number of
topics relevant to modern cosmology. More detail can be found in
several excellent textbooks
[1,
2,
3,
4,
5,
6,
7].
Throughout the lectures we have borrowed liberally (and sometimes
verbatim) from earlier reviews of our own
[8,
9,
10,
11,
12,
13,
14,
15].